Well, you'd be wrong. Loser.
It's from 'The Saint', set in Jolly Olde during the 1960s....
It wasn't just the logo for Starfleet that was stolen from the past (as I mentioned in last night's post about the Country Music awards), it was also the fashion designs.
Obviously whichever intergalactic Edith Head was responsible for coming up with the design for the Starfleet uniforms, they must have found their inspiration from the 20th Century. The uniforms on the left were worn by the elite force of mercenaries, technicians, and perhaps even scientists who worked for Keith Longman on his cryogenics experiment.
A smart move on the part of Mr. Longman - none of his men wore a red shirt, thus insuring that they wouldn't die if they went behind a rock on the estate!